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Day 390: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 25 (same type asked 11 times) See all 11 of this type

    75
    The value of ∫−π/2π/2cos⁡2x1+3xdx\int_{-\pi/2}^{\pi/2} \frac{\cos^{2}x}{1 +3^{x}}dx is:

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  2. Question 2

    Limits and Continuity. Asked once: 13 Apr 2023 (same type asked 11 times) See all 11 of this type

    159
    If lim⁡x→0eax−cos⁡(bx)−cxe−cx21−cos⁡(2x)=17\lim_{x \rightarrow 0} \frac{e^{ax}- \cos(bx) -\frac{cxe^{- cx}}{2}}{1 - \cos(2x)}= 17, then 5a2+b25a^{2}+b^{2} is equal to

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  3. Question 3

    Binomial Theorem. Asked once: 2021 Paper 7 (same type asked 11 times) See all 11 of this type

    90
    If (2021)3762(2021)^{3762} is divided by 17, then the remainder is

  4. Question 4

    Three Dimensional Geometry. Asked once: 25 Jun 2022 (same type asked 11 times) See all 11 of this type

    77
    Let QQ be the mirror image of the point P(1,0,1)P(1,0,1) with respect to the plane S:x+y+z=5S:x + y + z = 5. If a line LL passing through (1,−1,−1)(1, - 1, - 1), parallel to the line PQ meets the plane SS at RR, then QR2QR^{2} is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 31 Jan 2024 (same type asked 10 times) See all 10 of this type

    74
    The distance of the point Q(0,2,−2)Q(0,2, - 2) form the line passing through the point P(5,−4,3)P(5, - 4,3) and perpendicular to the lines r→=(−3i^+2k^)+\overrightarrow{r}= ( - 3\widehat{i}+ 2\widehat{k}) + λ(2i^+3j^+5k^), λ∈R\lambda(2\widehat{i}+ 3\widehat{j}+ 5\widehat{k}),\ \lambda\in\mathbb{R} and  r→=(i^−2j^+k^)+\ \overrightarrow{r}= (\widehat{i}- 2\widehat{j}+\widehat{k}) + μ(−i^+3j^+2k^),μ∈R\mu( -\widehat{i}+ 3\widehat{j}+ 2\widehat{k}),\mu\in\mathbb{R} is

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